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    Towards Conformal Capacities in Euclidean Spaces

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    This paper addresses the so-called conformal capacities in Rn\mathbb R^n, n≥3n\ge 3, through comparing three existing definitions (due to Betsakos, Colesanti-Cuoghi, Anderson-Vamananmurthy-Fuglede respectively) and studying their associated iso-capacitary inequalities with connection to half-diameter, mean-width, mean-curvature and ADM-mass, Hadamard type variational formula, Minkowski type problem, and Yau type problem.Comment: 33 page
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